Water damage/mould wooden outbuilding
Uninsulated wooden outdoor "summerhouse" looks like it needs a coat of something pronto. Are there any products that can be used in the winter?
Any treatment probably wouldn't work on wet or damp wood, so I think you would be best advised to wait until the Spring when the wood has had a chance to dry out. A couple of months or so wait won't hurt.
North East Somerset - Clay soil over limestone
I would wait until a dry spell in spring/summer and then put a de-humidifier in there for a bit before treating the wood.
Gardening in Central Norfolk on improved gritty moraine over chalk ... free-draining.
the enduring gardener
There's probably some marine based sealant that will adhere to damp surfaces but I'd probably wait til spring too. Maybe some guttering will help between now and then if it hasn't got it already.